Problem: Simplify; express your answer in exponential form. Assume $k\neq 0, y\neq 0$. $\dfrac{{k^{5}}}{{(k^{-1}y)^{-4}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${k^{5}}$ to the exponent ${1}$ . Now ${5 \times 1 = 5}$ , so ${k^{5} = k^{5}}$ In the denominator, we can use the distributive property of exponents. ${(k^{-1}y)^{-4} = (k^{-1})^{-4}(y)^{-4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{k^{5}}}{{(k^{-1}y)^{-4}}} = \dfrac{{k^{5}}}{{k^{4}y^{-4}}}$ Break up the equation by variable and simplify. $\dfrac{{k^{5}}}{{k^{4}y^{-4}}} = \dfrac{{k^{5}}}{{k^{4}}} \cdot \dfrac{{1}}{{y^{-4}}} = k^{{5} - {4}} \cdot y^{- {(-4)}} = ky^{4}$.